If M is a set of five numbers p, q, r, s, and t, is the range of numbers in M greater than 5?
(1) The average (arithmetic mean) of p, q, r, s, and t is 5.
(2) p −r > 5.
What's the best way to determine which of the statement is sufficient?
OA B
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If M is a set of five numbers
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Let's solve this problem by coming up with easy examples:
Statement 1
This tells us that $$\frac{p+q+r+s+t}{5}=5$$ We could have 3, 4, 5, 6, and 7 as the numbers in M, giving us a range of 4, making the answer to the question "no, the range of M is not greater than 5. However, we could also have 1, 3, 5, 7, and 9 as the numbers in M, giving us a range of 8, making the answer to the question "yes, the range of M is greater than 5. Insufficient.
Statement 2
If p - r > 5, then p is 5 greater than r. This means that the range of p and r is greater than 5. Even if p is the greatest number in M and r is the smallest number in M, that makes the range of all the numbers in M greater than 5. If another number in M is greater than p or smaller than r, that makes the range even bigger. So the range of M is greater than 5. Sufficient.
Statement 1
This tells us that $$\frac{p+q+r+s+t}{5}=5$$ We could have 3, 4, 5, 6, and 7 as the numbers in M, giving us a range of 4, making the answer to the question "no, the range of M is not greater than 5. However, we could also have 1, 3, 5, 7, and 9 as the numbers in M, giving us a range of 8, making the answer to the question "yes, the range of M is greater than 5. Insufficient.
Statement 2
If p - r > 5, then p is 5 greater than r. This means that the range of p and r is greater than 5. Even if p is the greatest number in M and r is the smallest number in M, that makes the range of all the numbers in M greater than 5. If another number in M is greater than p or smaller than r, that makes the range even bigger. So the range of M is greater than 5. Sufficient.
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